I used mplayer -options url://to/radiostation to listen to internet radio for some time. However I'd like to use another software for this. What do you use and what do you consider the advantages of this software?

Personally, I enjoy Amarok, and usually play streams in it. http://amarok.kde.org Many streams can be added via the script engine (Cool Streams and such), and individual streams can be added from the menus: Playlist > Add Stream. If you want to reuse that stream, save the playlist with the disk icon on the bottom of the playlist, then right-click to rename with an appropriate stream name if you want.

Any player can play a radio stream, the idea is to find the radios that you want.

After trying different ways of listening to internet radio, I think the best way is to create your own playlists of radio stations and then play them in your favorite music player and benefit from all the player's enhanced features, instead of using already compiled lists provided by a limited "radio player", while many radio stations are usually full of pub or plainly stupid, and the big number does not help finding the best ones. Better find them and save the ones you want in a playlist.

In order to find radios, there are a lot of ways, the internet is full of them. A radio player can be an initial way to find some radios, but searching the internet is a good way to refining criteria. One can go to a dedicated site like this, this or very comprehensive, like this and others, or search by different criteria (like high bitrate, and get something like this).

Many radio stations provide a pls or similar file that can be opened, saved or added into a larger playlist. The way the stream location is provided may vary.

Or the stream link may be visible:

And open URL/Location in an audio player.

Doing this for the best radios you find may lead to a long playlist that you can save and share. (Here are my present best radio playlists for jazz and classical music.)

To play such playlists better use a light and good audio player that would load/buffer instantly like Deadbeef or Audacious. VLC will do fine. I prefer DeaDBeeF (easy manipulation of playlists is important here).

I find this method very comfortable, for it gives easy access to what you most like and to change between stations.